AD-AI72 825 HOLOGRAPHIC PROPERTIES OF DNP-128 PHOTOPOLYNERS(U) DUKE 1/1UNIV DURHAM NC B D GUENTHER ET AL 85 SEP 86ARO-23284 i-PH OAALa-86-C-0885

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NATIONAL BUREAU OF STANDARDS 1963-A

11 jgj

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N TITLE

HOLOGRAPHIC PROPERTIES OF DMP-128 PHOTOPOLYMERS

O TYPE OF REPORT (TECHNICAL, FINAL, ETC.)

FINAL

AUTHOR (S)

B. D. Guenther and William Hay

DATE

9/5/86

U. S. ARMY RESEARCH OFFICE

CONTRACT/ GRANT NUMBER

DAALO3-86-C-0005

INSTITUTION

DUKE UNIVERSITY

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HOLOGRAPHIC PROPERTIES OF DMP-128 PHOTOPOLYMERS

12 PERSONAL AUTHOR(S)

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Final I FROMLJ,,J5/TO j2/3J/8[ September 5, 1986 I 4216. SUPPLEMENTARY NOTATION The view, opinions and/or findings contained in this report are those

* of he authr(j) and sh uld not be const ugd as an Efficial Department of the Army position,TV n 'l r ig _ n r •

tP £ e I n n -_ i n L- .cz -- n n c grp~ n -it -g- r h v - P rhl r im " _r,Jf gf l t e n

"7. COSATICODES 18. SUBJECT TERMS (Continue on revtrse if necessary and identify by block number)FIELD GROUP SUB-GROUP

i 19 ABSTRACT (Continue on reverse if necessary and identify by block number)* The holographic properties of the photopolymer DMP-128 produced by Polaroid werei measured. Holograms with a diffraction efficiency of 90% and index modulation in excessi of 0.06 was achieved. Both surface relief and volume phase modulation were observed toI be present. Wavelengths and angular sensitivity were measured. Handling and processing

properties were discussed.

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cop,HINSPECTED

CONTENTS

Chapter 1. INTRODUCTION ...... ................ 1

Chapter 2. THEORY .... ......... .... .... ... . 3

2.1 Holographic Theory . . . .. 3

2.1.1 Interference ........ ............... 3

2.1.2 Hologram formation ....... ............. 6

2.1.3 Hologram reconstruction ..... ........... 9

2.2 The Material ....... ................. 1S

2.2.1 Material parameters .... ............. 16

2.2.2 Shrinkage of the emulsion ... ........... 19

Chapter 3. EXPERIMENT AND ANALYSIS .... ............ 22

3.1 The Experimental Set-up .... ............. 22

3.2 Film Preparation and Processing ... ........... 23

3.3 Measurements ...... ................ 24

3.3.1 Spectral transmission of the system . . . . ... .. 24

4 l

3.3.2 Diffraction efficiency .... ............ 24

3.4 Data and Analysis ...... ............... 26

3.4.1 Diffraction efficiency .... ............ 26

3.4.2 Angular and wavelength sensitivity . ........ 32

3.4.3 Shrinkage ...... ................ 36

3.4.4 Resolution ...... .. ............... 37

3.4.5 Handling and processing ... ........... 37

V'.

Chapter 4. CONCLUSIONS ....... ................. 39

4 4.1 Suggestions for Further Research ... ........... 39

References .......... ...................... 41

.p.

LIST OF FIGURES

Figure 2-1. Interference pattern of two intersecting plane waves . ..... 5

Figure 2-2. Typical geometry for forming gratings. ..... ........... 6

Figure 2-3. Geometry of plane wave interference in a recording medium. ..... 7

Figure 2-4. The propagation vectors j and & of the reference and signal waves and

their relationship to the grating vector I Their respective obliquity

factors are also shown .......... ... ......... 12

Figure 2-5. q/Iq0 vs. 6-angular and wavelength sensitivity of lossless phase

gratings ......... .................... 14

Figure 2-6. A plot of V vs. E for the ideal recording material--lines of constant V0

are shown. ....... ................... 17

Figure 2-7. A plot of V4 vs. V for the ideal recording material--lines of constant E

are shown. ...... ... ................... 18

Figure 2-8. Geometry of shrinkage. (a) Before. (b) After .. ......... 20

Figure 3-1. Experimental set-up to form diffraction gratings .. ........ 22

..Iii.

n--

Figure 3-2. Spectral transmission for the glass substrate and for the exposed polymer

on the glass substrate ....... ................ 25

Figure 3-3. V'vs.E fore = 0and0 = 30. V =.97..... . ....... 27

Figure 3-4. \ vs. E for0 = 0 = 16. V = 1.0 ... ........... 29o I 0

Figure 3-5. Vvs.E for0 = 0and0 = 9. V =.99, V =.85,V0 R 0

=.32 ......... .................... 30

Figure 3-6. V-vs. Vfor0 - = 16. E - 5.0 ... ........... . 31

Figure 3-7. Photograph of surface relief in hologram with 0 = 0 and 0 = 9.1t 0

Magnified 700 times. ..... ................ 32

Figure 3-8. Angular sensitivity measurements for 0 = 0 and 0 = 30. E = 12.1,it 0 0

18.2 ......... ..................... 33

Figure 3-9. Angular sensitivity measurements for 0 = 0 and 0 = 9. E =Rt 0 0

15.8 ......... ..................... 34

Figure 3-10. Angular sensitivity measurements for 0 = 0 = 16. E =R 0 0

15.8 ......... ..................... 35

iv *

Figure 3-11. Wavelength sensitivity measurement--q vs X..............................36

Chapter 1. INTRODUCTION

aver since Denis Gabor discovered the principles of wavefront reconstruction (or

holography) in 1948, efforts have been made to improve the quality of the reconstructed

holographic image. In the early 60's, Leith and Uptanieks improved the performance of

holography by using separate object and reference beams [1]. The invention of the laser shortly

thereafter spurred increased research activity in holography as more powerful coherent sources

made quality images practicable. As in most developing technologies, a major field of

continuing interest is the search for better materials. This thesis is dedicated to the

characterization of a promising new development in holographic recording materials: Polaroid's

DMP-128 holographic recording system

Several material systems are suiable for the recording of holograms, but there are

significant differences in the performance achieved by each. These differences pervade every

aspect of the material: storage, preparation for exposure, exposure, processing and subsequent

usability. Important factors which must be known before the desired hologram can be made

include film sensitivity (analogous to speed in photographic film), linearity of the response to

light, maximum diffraction efficiency, signal-to-noise ratio, wavelength and angular sensitivity

and resolution of the film. Each of these parameters vary from material to material and can

also vary with the thickness or processing of one material. Some of the presently used materials

include silver halide film, dichromated gelatin, photopolymers, thermoplastics and photoresists

[2]. Each of these has its advantages and disadvantages. Dichromated gelatin, the present

industry standard, is capable of very high diffraction efficiency, but great care must be exercised

in processing and developing the hologram. DMP-128 photopolymer exhibits some very

desirable qualities, including long shelf storage time, high efficiency and ease of processing.

Chapter 2 of this thesis will include a review of the principles of holography and theory of

characterization of holograms. The experimental set-up and scope of the experiments along withr1

*' -1-

S Si

ii the results and analysis comprise Chapter 3. Conclusions and suggestions for further research

are reviewed in Chapter 4.

S.

-- 2-

""p. " ;

Chapter 2. THEORY

Holography is the science (and art) of recording the phase and intensity information in a

light signal by means of interfering the signal with another, coherent beam and storing the

resulting interference pattern (a concept very similar to that of modulating an electrical carrier

frequency with a signal frequency). While this work is concerned mainly with one material used

to record this information--Polaroid's DMP-128, a brief review of the principles of holography is

in order before proceeding. This review will be constrained to signal and reference beams

consisting of coherent plane or spherical waves. A description of the DMP-128 holographic

recording system will follow, along with an enumeration of material concerns and parameters.

2.1 Holographic Theory

* 2.1.1 Interference

For a monochromatic wave of frequency f, the electric field V" can be expressed as

- = icos(2wft + 4o), (2.1)

where i is the amplitude of oscillation and 4 is the phase [3]. The phase 40 contains the spatial

dependence of the wave. When two or more sinusoidal waves are summed, the resulting wave

is also sinusoidal, yielding

i cos(2uft + +I) + i cos(2wrft + *2) + . icos(21rft + 4), (2.2)1 1 22

or in complex notation,

Re[iexp[i(2irft + 6) )] + Re[i2exp[i(2rft + +)A]] + (2.3)

= Re[iexp[i(2rft + 40)1].

The latter form is advantageous for most mathematical manipulation and shall be used here,

* .3-

-

N adopting the common convention of dropping the "Re[ ]" while still assuming its existence. As

the frequency will always be held constant in this work and relative, not absolute, phase is the

'* important factor, the temporal phase term exp(i2irft) will be dropped, leaving

iexp(i*4I) + i2exp(i4 2) + .. = iexp(i4) = a, (2.4)

where i is the complex vector amplitude. Complex quantities will be denoted by bold-face type.5,.,

The intensity I of a wave is defined as the time average of the energy flow per unit time

per unit cross-sectional area,

I = IJ2s<' >, (2.5)P

where s is the speed of light in the medium and E is the dielectric constant. In holography, the-4."

intensity I is alternately defined as

I = 2< - >, (2.6)(2.6

which is the square of the amplitude of the wave, or

a ai'i~i. (2.7)

For the purposes of holography, we are generally concerned with only two waves--a reference

and an object wave. In this case, Eq. 2.7 becomes

= ii = i I + i I + 2'i cos(4 -4 ) (2.8)1 1 22 12 2 1

- I + I + 2(ii2COS(OO2 -(0)).1 2 1

In our experimental set-up, both waves are polarized parallel to one another; the dot product

reduces to scalar multiplication of the amplitudes in this case and shall be written in that form.

-4-

% %

In the special case of forming diffraction gratings, both of these waves are plane waves.

Wave normal wove normal*no. I no. 2

F?. 8e 8 F

.,F2 F 0F N F 1

JRgur 2-1. Interference pattern of two intersecting plane waves.

This is presented graphically in figure 2-1. The wavefront crests, separated by the wavelength

X., are represented by F and F for wave number 1 and wave number 2, respectively. Where

11

thesn two wavefronts intersect, they interfere constructively, resulting in planes of the highest

intensity, depicted by the close spacing of the vertical lines, which bisect the incoming wave

normals. These planes lie perpendicular to the plane of the paper. It is this varianc in

intensity which is recorded by the hologram. The relative intensity of the two beams is known

as the K-ratio, where

%K-I I . (2.9)1 2

The importance of K can be seen by considering the maximum and minimum intensities of the

44

*..,.S. -1-. 5 ..,~emc -- r'f w nen cn laew vs

interference pattern. From Eq. 2.8 it cani be seen that when K -1 (corresponding to 1I = 1)2

the intensity of the fringes varies from zero to 41. For K s' 1 (corresponding to I I 12), the

intensity neither falls to zero nor rises to twice that of the total incident intensity. The fringe

visibility V is a measure of this fringe contrast and is defined as

sa" 'min2m

= (2.10)

1 +1I K+ 1

2.1.2 Hologram formad1on

N1

object beam

Figure 2-2. Typical geometry for forming gratings.

A typical set-up for forming diffraction gratings is shown in figure 2-2. The film will be

assumed to be in the z-y plane with the z-axis as the normal to the surface; beams are assumed

to propagate in the y-z plane. The laser is split into two beams which are then spatially filtered

. with a microscope objective and pinhole. Next both beams are collimated and directed onto the

recording medium. The reference and object beams intersect the film plane at angles 8 andRa

*0,1 respectively, as measured from the normal. Depending on the thickness T of the material

and the angles of incidence, the resulting hologram is classified as either a plane (thin) or

volume (thick) hologram. The difference and the consequences will be explained later.

Inside the medium the interfering beams produce planes of periodically varying intensity

Y fK

Figure 2-3. Geometry of plane wave interference in a recording medium.

which extend parallel to the x-axis. The resulting geometry is shown in figure 2-3 [4). Upon

'.9

Ii,

.7.. entering the medium, the reference and object beams are refracted according to Snell's law and

" propagate through the medium at angles 0 and 9 defined by

~ .. . . . . ' . . . . . . •

sine sineR On

= , (2.11)

sine sineI1 0

The resulting amplitude inside the medium is

a = a exp(-i2,r/k(sinO y+cose z)] + a exp[-i2ir'/(sinO Y+cose Z), (2.12)* R.f R R. 0 0 0

and the intensity from Eq. 2.8 becomes

I = I 1+ I + 2(1 R 1) cos[2i/X[(sine - sine )y + (cose - cose )zJJ, (2.13)

where I and I are the intensities of the reference and object beams. At the air-medium

interface, the fringe spacing in the y-direction d isy

d- (2.14)Y

sine - sine0 R

obtained by setting z= 0 and solving for adjacent intensity maxima. The fringe planes bisect R

and 0 and the angle they make with medium boundary, called the slant angle4, is

0 +e

if R 0

- (2.15)

2 2

N- The distance between the crests is called the fringe period d and is equal to

d - d sin,0. (2.16)

The grating vector k is perpendicular to the fringe planes and has the value

K - 2w / d. (2.17)

4-

In order to record the interference pattern described above, the medium must respond in

some way to the intensity of the light. This can be done either by changing the real

transmittance, the thickness, or the index of refraction of the medium [3]. The first type is

known as absorption hologram, while the latter two are known as phase holograms. Also

known as surface relief, the thickness variation changes the phase by controlling the distance the

beam propagates in the medium; the phase is retarded for rays which travel farther in the

material, because the higher index of refraction creates a longer optical path length. In the last

case, the incoming rays are diffracted by the changing index of refraction in the medium. All

three effects may be present in any hologram, but one type usually predominates. DMP-128

changes index of refraction with exposure and records the fringes as a spatial modulation of the

- index of refraction, n = n + n (y,z). In addition to the change of index of refraction, thereo0 m

may be some surface relief involved due to mass transport and changes in density.

2.1.3 Hologram recontrtunilon

A hologram is considered to be a volume hologram if light diffracted by it during

reconstruction passes through several fringe planes [2]. If a hologram is too thin or the fringes

are spread too far apart, the diffracted beam interacts with only one or two fringes and the

hologram is essentially a planar construction. The parameter Q is used to distinguish between

9. volume and plane holograms [41, where

2

* = 2w)L T/nd. (2.18)a

While the transition between volume and plane holograms is somewhat gradual, it is generally

accepted that for 0 2t 10, the holographic properties are based on volume diffraction.

2.1.3.1 Plane holography In the case of a thin hologram, Eq. 2.13 reduces to

(112)

0I + IR + 2(1 I ) cos[2arrA(sinO - sinR )y], (2.19)

.9-

JINL

as the hologram is negligibly thin in the z direction. The recording medium is modulated

proportionately to the intensity I(y), causing a phase shift +(y) on a plane wave propagating

through the developed hologram [1], expressed by

(Iy) a (y) (2.20)

012)= I + I + 2(1 1 cos[2r/)X(sine - sine )y]0 R O R 0 Rt

=4 + 4 1cos[2ir/x(sine ° - sine )y].

The light passing through the developed hologram relative to the light incident on it is called the

transmittance. In the case of a lossless phase hologram, the transmittance is a complex number

of unit value. Thus the transmittance t of a thin hologram is

t = exp(i4 )exp[i4 cos[(2,w/)(sine - sine )y ] . (2.21)

0o 0 it

Neglecting the constant phase factor which has no imaging effect, we can express the

transmittance as a Fourier series

+a

t - i J (4 )exp[(in2iA)(sinO - sine )y], (2.22)al0 Rt

where. J is a Bessel function of the first kind and nwh order. Each of the summed terms

corresponds to a diffracted order of the signal beam [5]. The first diffracted order is

represented by the term for n = 1:

t M (4 )exp[(i2ir/X)(sinO - sine )y], (2.23)

1 1 0 RtI of which the amplitude is simply J For a reference beam of unit amplitude, the maximum

amplitude of the first order Bessel function is .582, thus the maximum diffraction efficiency for

-10-

2 2

thin phase holograms is a = .582 or 33.9%. This relatively low maximum diffraction

efficiency would be severely limiting to practical applications of holography where high

efficiency is required, but as is shown in the next section, higher efficiencies are obtainable in

volume holograms.

2.1.3.2 Volume holography In efficient volume holograms one must consider the attenuation of

the reference beam when analyzing diffraction. Kogelnik adapted coupled wave theory analysis

to holographic volume diffraction gratings in order to account for the high diffraction

efficiencies obtainable [4]. His analysis is followed here.

A wave propagates in the medium according to the wave equation

2 2V a + k a = 0, (2.24)

where k is the propagation constant defined by

k - 2an / k, (2.25)

assuming a lossless medium. The index of refraction is assumed to vary sinusoidally with an

average value n and an index of modulation n, or0 I

n = n + ncos(K 9). (2.26)0 1

where 9 is a unit vector in the y-direction. The incident reference wave a can be written as

a = R(z)exp(-ij-9), (2.27)

where j is the direction of wave propagation. Similarly the amplitude of the diffracted signal

wave a is

as = S(z)exp(-iy9), (2.28)S

%' .fo.

where i is the direction of propagation of the diffracted wave. and I and their relationship to

Y K

1

ft

M -24. The propagation vecton and i of the referene and sigal waves and their relationship to theStating vecor K. 7beir respective obliquity factors are also shown.

t are depicted in figure 2-4. These waves are coupled by a transfer of energy between them.

The amplitude of the total electric field is thus

a - a + a - R(z)exp(-i-t) + S(z)exp(-i& '). (2.29)

If S differs from the Bragg angle 0 by A$ or the reference wavelength differs from the-. ' 0

recording wavelength by AX, the Bragg condition is not met and a "detuning" or "dephasing"

occurs. The dephasing measure 8 is defined as

2

a - As Ksia( ° -)- Ak K /4mrn. (2.30)

The obliquity factors c and c are related to the propagation of the reference and signal wavesIt s

in the z direction, respectively, and are given by

* 12

c - cose (2.31a)

R

c cose - cos4,. (2.31b)S

nd0

They are shown in figure 2-4, using 2wn/k.

When the coupled wave equation is solved for the case of phase transmission gratings-

R(z=0)= 1, S(z=0)= 0-we obtain the amplitude of the emerging signal wave

(L#2) 2 2 (12) 2 2 (1/2)

S(T) -i(c I/c) exp(-it)sin(v + t) /(1 + 6/h ) , (2.32)

where"-" (i/2)

v = wn ITA (c Rc) (2.33)

4 and

B- T/2c. (2.34)

The diffraction efficiency q is defined as the fraction of incident power diffracted into the signal

wave, which is written asa

= (ic/cR )SS. (2.35)

This can now be calculated to be

2 2 2 (1/2) 2 2

-. = sin (v + /(I + t /v (2.36)

In the case when the fringe planes are perpendicular to the medium boundaries (4 = ir/2), this

reduces to:

-13-

2- sin (an T/Xcose0). (2.37)

From Eq. 2.37 it can be seen that the theoretical maximum diffraction efficiency of volume

phase holograms is 100% for an IT/)cos0 = (2x + 1)r/2, for any integer x.

Also of interest are the angular and wavelength sensitivities of a hologram. When AX - 0,

the angular deviation can be expressed as

I - AKdsin(* - e0)t2cs. (2.36)

Similarly, for AS 0, the wavelength deviation can be expressed as

2

- AXK d/8vnC (2.39)

i~S.

0 2

-PIP- 2 .,0v.Ewuaw aent mtv fluspa mip

q. -,

difato efiiny or inrasn vauso ,tesnstvt uv arosadsd oe

0.4

.. 2

0 I 2 3 ,

11g 2-S. q/qo vs. i--ngular and wavelength sensitivity of loslesa phs gratp.

~The sensitivities can be shown as a function of v as in figure 2.5, where 1iI/I 0 is the normalized

diffraction efficiency. For increasing values of w, the sensitivity curve narrows and side lobes

-.14.

become much larger. Increasing v can correspond to increasing index of modulation, thickness

or incident construction angle. For unslanted gratings, the half-power bandwidths can be

approximated by

2A d/T (2.40s). (12)

and

2AX cot(O)d/T. (2.40b). (1i2)

These bandwidth calculations are only approximate as Kogelnik's theory assumes that A8 << I

in order to solve the wave equation (Eq. 2.24) for the coupled signal and reference waves.

2.2 The Material

The Polaroid DMP-128 holographic film is a photopolymer system which produces phase

holograms. Photopolymer systems for holography were first developed in the late 1960's by

Hughes Aircraft [6]. Another notable commercial development of a similar system was by

Booth at Dupont.

A typical photopolymer system consists of a polymer (often called the binder), a monomer

(or monomers) and a dye [6]. The polymer adds physical strength to the emulsion and aids in

the coating of the emulsion substrate. The dye absorbs the incident light, thereby providing the

initiation energy for the photochemical reactions which lead to the polymerization of the

monomer. One photon can provide enough energy to form a molecule chain of hundreds of

monomer units, accounting for the good sensitivity of the DMP-128 material [7]. The

polymerized molecule has a different index of refraction from that of the monomer, resulting in

a gradient in the index of refraction in the material responsible for hologram formation. The

frequency range over which the Polaroid system is sensitive is determined by the absorption

spectrum of the incorporated dye and can thus be altered by the selection of specific dyes.

.,1.

,....~

~.L.~L'~i.N. . * ... . -rn. -4. -

While the exact mechanism of fringe recording in DMP-128 and other photopolymers is not

'- known, several basic tenets are postulated. When light strikes the photopolymer, the monomers

in that region join to form large chains of molecules. This depletion of the monomers in one

region causes a gradient in monomer concentration. The monomers in the higher concentration

regions tend to diffuse to the regions of lower concentration, where they are also polymerized.

This movement of the monomers and polymerization of the material could cause thickness

variations in the material which would yield a surface relief effect. The polymerization into

large molecules is known to cause a change in index of refraction in the bulk material, so this

effect can form volume holograms in which the index of refraction is selectively modulated.

When the material is illuminated with white light after exposure, this thickness variation or index

of refraction modulation is frozen by the polymerization of all the remaining monomer.

Shankoff has theorized that the diffraction in dichromated gelatin is caused by miniscule cracks

in the emulsion which are filled with air [8]. This is also a possibility in DMP-128.

DMP-128 is available in three formulations which contain different dyes: one is sensitive in

s:; the blue region of the spectrum, one in the green and the other in the red. In this report, the

discussion will be limited to the red-sensitive film. The film is also available in varying

thicknesses ranging from three to twenty microns, but this report will be confined to seven

micron emulsions. The emulsion has a bulk index of refraction of 1.53 [91 and is supported on

a flint glass substrate which has an index of refraction that closely matches that of the

- photopolymer.

2.2.1 Material parameters

A holographic recording material has several associated parameters which quantify its

response to the interference pattern which forms the hologram. Among these are sensitivity,

linearity and resolution. These parameters must be considered during hologram formation in

order to achieve the desired results for hologram reconstruction.

% -l%

The sensitivity S is a measure of the amount of change in the material as a function of

exposure energy [3]. It is defined by the equation

SSE EV, (2.41)

, where E is the average exposure over the hologram. For an ideal hologram where the1',2 0

* .~reconstructed wavefront is linearly proportional to the original object wave front, S is

independent of V and E. In real recording materials, however, S is not independent and0

linearity is a non-quantitative measure of how S depends on V and E. A plot of vs. E

'S

0.80V .

0..80.6

,'-

.0.6

... 0.4-

"..

0.2 0.2

o .

0• -,, . 0 2 3 4 5

EO (arbitrary unit)

Ilgu-e 24. A plot of vs. E for the ideal recording material-lines of constant V are shown.0

with various constant values of V is shown in figure 2-6. The characteristics of each value of V

are perfectly straight, indicating linear S. The analogous plot of V vs V for constant E is- 0

shown in figure 2-7.

In an ideal material, all of the incident light would be diffracted into the emerging signal

V7 .17-

.+,r. a 'a *',*.

.~0.6 -

'..

'9.

"

!I o0.6-

'd0.4-

0.2 -

0

0 0.2 0.4 0.6 0.8 1.0V

71guze 2-7. A plot of '4 vs. V for the ideal recording material-lines of constant E are shown.0

beam. Unfortunately, even with perfect holographic technique, the signal is accompanied by

some noise due to imperfections in the hologram and nonlinear recording. The major film

imperfection, neglecting gross macroscopic faults, is that of surface modulation. While the

surface effect can itself form holograms, this causes a generally undesired phase shift in volume

holograms. This effect can be minimized by use of index-matching. Nonlinearity is a more

serious problem. For nonlinear S, the v' vs. E 0 and V curves can be approximated by

polynomial expressions. The first order term accounts for the desired linear response, but the

quadratic and higher order terms cause ghost images and halos. In the case of the diffraction

grating, the higher order terms diffract light into other orders much like a Fresnel zone plate or

*Ronchi ruling.

. Recording resolution is the measure of minimum fringe spacing in the material [3]. Fringe

frequency v is the reciprocal of the period,:--.

; ','.-,,",';':.':':-:.":'':"'","'''"':,'',"":':"":";'' ''-'-"'::'.:" ''':'"" " ""-

v= ld. (2.42)

For transmission holography, the maximum frequency needed can be found by taking most

extreme angles possible in the constructing geometry. Trivially, for the reference and object

beams incident at the same angle, v - 0; for incident beams with the maximum interbeam angle

B = -e = ir/2, v = 2/X . Letting X = .6328 pLm, 0 < v < 3160 cycles/mm. In reflectionRa O a

holography, where the fringe planes are parallel to the medium surface, the fringes are separated

by

XX

d (2.43)1 2 (11) 2 2 (1 )

2(1 - sin 0) 2(n -sin 0)

Letting n = 1.5 and ) =.6328 pm while varying 0 from /2 to 0, we obtain 4700 <S0 a S

(v = lid) < 5700 cycles/mm. If a recording medium can not support as high a resolution as isz a

required, the image will be degraded.

2.2.2 Shrinkage of the emulsion

One difficulty inherent in many holographic media is that of swelling and shrinkage. This

change in size can be quite detrimental to the accurate reconstruction of the recorded image.

The activation and processing steps generally add to or deplete various constituents in the

.. . emulsion. In dichromated gelatin this can actually increase the thickness of the emulsion by

three or four times at certain stages of the processing [2]. Silver halide films tend to shrink by

approximately 15% of pre-exposure thickness as a result of normal development [3]. DMP-128

also exhibits a certain degree of thickness variability as a function of processing.

*1' In general there is little lateral shrinkage in a hologram, as the emulsion is stretched out on

a rigid substrate which prevents this. Excessive lateral shrinkage or swelling would result in the

-19-

5, -,

%. . . .. . . . . . . . . .

oSJ~r

KA,/

(a)

1-gon 21. Geoumtry of -rinkage. (a) Before. (b) After.

tearing or folding of the emulsion and the probable destruction of the hologram. As shown in

figure 2-8, the major effect of shrinkage is the tilting of the fringe planes [10]. The fringe

spacing in the y-direction d remaisconstant due to lack of lateral shrinkage, but the change in7

thickncs results in a change in the slant angle along with the grating period. Cosmquently, the

Bragg angle changes and the hologram does not reconstruct exactly. In effect, the hologram acts

as if it had been formed using different construction angles, symmetric around the new fringe

planes. While the original slant angle was

- ( -) / 2 -a=Can(h / T), (2.44)

the new slant angle +' is

S(O' 0 - o) I 2 - arctan(h T'), (2.45)

Also, retaining the fringe spacing along the y.axis,

- (2.46)

(sine + sie ) (siO' + sine' )

.20.

L M MR..*.

Solved simultaneously, these equations become

sine + sine = sinO' + sine' (2.47)0 it 0 R

and

V' 0 -o 0 ' -0e'o R o R arCtan(h/T)

(2.48)

2 2 arctan(h/sT)

where s = T'/T. For small angles, where sinx tanx = x, Eqs. 2.48 become

(1/3) (80 - 0R) = 8' - 8' (2.49a)0 R 0 It

0 0 =0 ' + 0 ' R (2.49b)

4-21-

Chapter 3. EXPERIMENT AND ANALYSIS

This chapter will describe the experimenal set-up and methods used in making holograms

with DMP-128. The data and results will then be presented and discussed according to the

, ,theory presented in Chapter 2.

3.1 The Eperimental Set-up

Holograms were formed using the Leith-Uptanieks geometry described in Chapter 2 and

~object beam

reference beam

11n3-1. Exumm wt-up to form ddiH d sminp

shown here in figure 3-1. Ile beam from the He-Ne laser (X 632.8 am) is split using a

variable beam-splitter and then spatially-filtered using 10x microscope objectives and 25 ILm

i pinholes. This removes any incoherent elements in the laser light. The beams are collimated

-. and directed onto the film, intersecting the film plane norml at anles of 0 and O for theIts Oa

4,,

nreference and object beams, respectively. Holographic lenses (gratings with focusing power) are

formed by eliminating the collimating lens in the object beam path, leaving a spherically

diverging wave as the object beam.

,:2

During exposure, the film is secured in a film holder adapted from Polaroid consisting of a

prism with a trough secured on the front face. The trough is filled with xylene (index of

refraction = 1.494) which holds the coated substrate against the prism by capillary action. In

order to prevent reflection at interfaces where the index of refraction changes abruptly (which

would cause additional interference in the material and result in a destructive "wood-grain"

pattern), the xylene, the substrate and the prism were all chosen with n = 1.5 in order to match

the index of refraction of the emulsion. The prism is also used instead of a glass plate to

prevent reflection from parallel surfaces back through the emulsion.

The variables of exposure were the angles of incidence, the visibility and the exposure time

(hence exposure energy). Pains were taken to keep all other variables such as activation,

flooding time and chemical processing as constant as possible. The film used during the course

of the experiments came from three separate batches, but is assumed to be uniform in

composition. The thickness of developed samples from two of the batches was measured with a

profilometer and found to be seven microns.

3.2 Film Preparation and Processing

Polaroid's DMP-128 requires activation by absorption of water before exposure and

development [7]. This is achieved in a reproducible manner by exposing the emulsion (which

has been stored in a very low humidity environment) to a controlled-humidity atmosphere for a

prescribed time period. The necessary time interval depends on the ambient humidity and on

the thickness of the material. The humidity is controlled using a saturated salt solution of

. calcium nitrate in a closed container. At equilibrium, the relative humidity above this solution is

51.0%; this remains fairly constant over a moderate temperature range around room

temperature. In order to insure equilibrium conditions inside the chamber, the solution is

constantly stirred with a magnetic bar and the air is circulated in a closed loop above the

solution. For optimum activation under these conditions, the seven micron emulsion is incubated

-23-A .. *J .4

for four minutes. In order to prevent evaporation or absorption of more water into the

emulsion after activation in the chamber is complete, the laboratory air is also maintained at a

relative humidity of 51 - 5% and the xylene, which is hydrophilic, is water-saturated.

After activation, the film is placed in the holder with the emulsion side to the prism and

time is allowed for all vibrations and air currents to cease. After exposure, the film is

illuminated with white light for two minutes to polymerize any remaining monomer and fix the

monomer gradient in the material. The light source is a 60 W tungsten bulb in a reflector held

8" from the film. To insure repeatability in case of any post-exposure monomer diffusion, a

ten-second delay is counted after exposure before the film is illuminated. Next, the film is

placed in the processing fluid for two minutes and then rinsed liberally with isopropanol or

methanol. Afterwards the film is dried in the vapors of boiling isopropanol for one minute.

3.3 Measurements

3.3.1 Spectral transmission of the system

Because the emulsion is coated on a glass substrate, the properties of the substrate must be

taken into account in determining the efficiency of the processed hologram. Also of interest is

the transmission characteristic of the polymer which has been flooded and developed, but which

has not been modulated by an interference pattern. A spectrophotometer plot of the glass

substrate and of the exposed photopolymer on the substrate is shown in figure 3.2. The glass

substrate begins to absorb the light around a wavelength of 360 nm and begins absorbing

strongly at 320 am. The photopolymer begins absorbing at 500 nm and absorbs at wavelengths

lower than 400 nm. This can be considered a baseline value for the scattering of light by the

polymer. In the spectral range used in this work, the absorption can be neglected.

3.3.2 Diffraction efficiency

Al! irradiance measurements were made with a Jodon light intensity meter held

.24.

V*. ,,V '.~ .--. 5 . 5- .. S a . . .

.0 a

0 Q

11tam 3-2. SPeWtra &Maaion for the ga= SubBMW and for to ezpoasd POlYWW eth ls subam.

perenicia to the beam. Measurements of the diffraction efficiency were made by

illuminating a I mm diameter circle in the center of the hologram. In order to account for

Prmne! reflection at the surface of the glass and possible absorption by the polymer, the beam

passing through a portion of the exposed polymer in which no hologram is recorded was

measured and considered to be the incident irradiance; all diffraction efficiency calculations are

made relative to this. In order to measure the angular sensitivity of the hologram, the film plate

was rotated through from 30 to 50 degrees around the constructing reference angle while

-25-

measuring the light diffracted into the first order.

. The wavelength sensitivity measurements* were performed using four different lasers with

different wavelengths. The diffraction efficiency was optimized for the 514.5 mm wavelength

and all other measurements were normalized relative to this value. The other wavelengths used

were 442, 488 and 632.8 nm. All measurements were made at the same incident angle. It must

be borne in mind that this is only an approximate measurement.

Another important concern is the type of mechanism responsible for the diffraction of the

incident beam--an index of refraction gradient or surface relief. If no thickness variation is

found, then the hologram may be assumed to be a volume hologram. A common method to

test for surface relief in holograms is to gate the hologram with a liquid of approximately the

.', same index of refraction; this is known as index-matching. The liquid fills in any thickness

variations and negates any effect of surface relief by eliminating any difference in optical path

length. This was done with xylene and glycerin (n - 1.5). The hologram surface (including

one coated with 150 Angstroms of gold in a vacuum evaporation chamber) was also inspected

with a metallurgical microscope and a scanning electron microscope.

3.4 Data and Analysis

3.4.1 Diffraction efficiency

The diffraction efficiency of a holographic material depends on a number of variables: the

exposure energy, grating period, material thickness and visibility can all be tailored to suit one's

needs. In manufacturing holographic optical elements, maximum diffraction efficiency is

(usually) desired; in making display holograms, linearity is important. The V vs. E and V

plots proposed by Lin [111 provide much of the necessary information.

T o. wavwaq& fmm masurm, wm sraioly palonmd by Tom Sum al ft Univmty of Ra'cu Opms DepuUeM.

.26-

* j s*i*~s ~ -'

q e l

Sqrt (eta)1.0-

0.0+-

* I

I-

0.00Ii

0 17 35 52 70Exposure (mJ/cm^2)

NMSM3-3. Vq' .E fore -O dO = 30. V-.97.

Shown in figure 3-3 is the plot of V vs. E for - 0 and O - 30 for a constant valuef0 R

of V - 0.97. The diffraction efficiency rises quickly with exposure to a maximum around 142

mJI/cm. The efficiency decreases again to roughly two-thirds the maximum efficiency at twice

the exposure. It remains fairly constant thereafter, rising again slightly for very high exposure

q, energies. The initial rise to high efficiency is approximately linear, indicating that the sensitivity

Is not strongly dependent on the exposure in that regime. The diffraction efficiency is high,

reaching a peak of 82.9%. According to Kogelnik's coupled wave theory, the efficiency should

.27-

peak and fall again to zero. This is not observed and there are a couple of possibilities for this.

Kogelnik's theory holds well only for holograms with high values of Q. The Q-factor for this

4 set of holograms is 28.5. While this value is greater than ten, which is quoted by Kogelnik as

the region in which the coupled wave theory holds, the cycling of the efficiency from zero to

one as the index of modulation increases is not always observed to happen unless 0 is very

large [12]. Another possibility is that of surface relief in addition to the volume effects. While

volume and plane holograms are theoretically distinct, the dividing line between them is blurred

and most holograms show some effects of both types. This is reinforced by the observation of

fringes in all of the holograms using the metallurgical microscope.

The plot of V' for 0 R - = 16 shown in figure 3-4 is very similar to the previous plot.at o2

The efficiency reaches a peak of 90.0% for an exposure energy of 6.7 mJ/cm and decreases to

an efficiency of around 50% at twice the exposure. The diffraction efficiency appears to rise to2

a second peak near E = 20 mJ/cm. The index of modulation of the hologram with exposure02

energy of 16.7 mJ/cm can be calculated to be .061.

Figure 3-5 shows a plot of V' vs. E for S = 0 and 0 = 9 and constant values of

visibility. For V = .99, the diffraction efficiency rises quickly to an apparent peak near 162

mJ/cm and then decreases much like the aforementioned examples. In agreement with Lin [10],

the diffraction efficiency for V = .85 rises more slowly than that for V = .99. The slope is

approximately linear, although not completely. Again, the peak efficiency is followed by a drop

and then a slow rise. The diffraction efficiency for V = .32 rises slowly, but quite steadily,2

only reaching a peak of less than 50% for an exposure of 50 mJ/cm before leveling off.

The other plot proposed by Lin [111 is a plot of Vq vs. V for constant E. An example of

this is shown in figure 3-6 for 0 = 0 = 16 and E = 5.0. The plot is almost linear, showing,a 0 0

only small dependence on visibility. For a hologram with a relatively uniform exposure

intensity, one can see the limits of linear recording from this plot. Many holograms, such as

%:4

16. -. , . . .. . - .. .. , •

Sqrt (eta)".; IcZ I I--0 0

0.00 6 12 18 25

Exposure (mJ/cm^2)p.,

lrm, 34. Vm.s .E fore - e - 16. V-1.o.0 R 0

diffusely-lit object holograms are fairly uniform in exposure, but not in visibility. For

holographic optical elements such as diffraction gratings, the visibility is constant and the plots

of V~ vs. E are more revealing.. 0

Several approaches were tried to resolve the question of the mechanism of diffraction.

. Index-matching produced inconclusive results. When index-matching using xylene, the

diffraction efficiency decreased from 61.2% to 1.7% on one hologram made with a total

-29-

" "- .

Sqrt (eta)10 I I I I I

-- A A

0 0

o0, oI ° I I I

-0 40 80 i20~Exposure (md/cm'2)

Har.4.V ,.Eto, ,,o-,e -9. v -.9,i.5,v -.32

0 R o

interbeam angle of 30 degrees (d - .80 Lm). This can not be due completely to negating any

surface relief as the maximum diffraction efficiency of such holograms is 33.9%. The hologram

also disappears when wetted with methanol or isopropanol and returns to the original diffraction

efficiency after drying. These liquids (with low surface tensions) may be filling in tiny cracks or

voids in the polymer which account for the change in index of refraction. This method of/hologram formation in phase gratings was proposed by Curran and Shankoff [81 for dichromated

gelatin and could also be present in the photopolymer. Index-matching was also performed

.30.

III I I

0.8-

0.7

0.6

0.5-

0.4-

0.3-

0.2-

"" 05

0.1--

0.00.0 0.2 0.4 0.6 0.8 1.0

Visibility

PIPM.3-C V"vs. V for 0 0 16. E " 5.0.It o 0

using glycerin (n - 1.5), a more viscous liquid. The observed diffraction efficiency of the same

. hologram decreased to 6.6% upon application of the glycerin. Assuming that the glycerine does

not penetrate the hologram as easily as do the alcohols and xylene, the smaller drop in

diffraction efficiency could be attributed to not filling in all or as many of the voids. Shankoff

noted that in dichromated gelatin the emulsion had pulled away from the substrate, creating

voids between the substrate and the emulsion. This could account for the higher diffraction

efficiency when gated with glycerin rather than zylene-having a higher surface tension, the

-31-

4-

M90m 3-7. Photo aph of suASM relief il hologrm with S - 0 1m S -0 9. Mapnified 700 dMes.a O

glycerin could not flow as well as the xylene and fill deep voids. A second hologram, with a

total interbeam angle of 9 degrees, originally had a diffraction efficiency of 71%, but fell to

12% when gated with glycerin and 4.5% when gated with xylene. The holograms were also

i. observed under a metallurgical microscope for possible thickness variations. Surface modulation

was visible in all the holograms, even the holograms with smaller periods. The relief was not

measurable, but appears to be less than one micron. Small scale surface roughness was also

visible in all holograms. A photograph of a hologram which was coated with a 15 nm layer of

-~gold in a vacuum evaporator is shown in figure 3-7. The period was measured to be 2.4 pm

which corresponds to the calculated value for the incident angles of 8 = 0 and 0 - 9. TheR 0

same hologram was viewed in a scanning electron microscope. The electron beam was visibly

destructive to the hologram and no surface relief could be seen, although surface roughness and

irregularities were visible at magnifications from 500 to 20000 times.

4. 3.4.2 Angular and wavelength sensitivity

Angular sensitivity measurements were made on four sets of slides with different incident

angles: O -0 and -0 9, O R 0and0 - 12, S W 0and S 0 30 andS -0 - 16.

-32-

% .jx?,

,," 1

-'.

Etae1. 0-

,-F- 2o

- -20 0 10Reconstr. Angle

Fismt 34. Angua eitivity meauremnt for 6 0 and 8 30. E =12.1, 18.2.

modulation, the side lobes are seen to increase as predicted by Kogelnik (4]. The half-power

bandwidth is 8 degrees for both; it should show no change for increasing efficiency and does

not. The calculated half-power bandwidth from Eq. 2.38a is 6.5 degrees. For the plot shown

4 in figure 3-9, the calculated half-power bandwidth is 19.6 degrees; when measured, it is 22

degrees. From these two plots, it can easily be seen that the angular sensitivity becomes much

*%' -, .. .

smle fo raeRnlso ni ect . nl

.33o

":'-"~~~~~~~~ ~~~~~ %hw ifgr - r w esrmnsfre n 0 o nraigidxo

Eta1.0' iiiiiliiiiiiiiiii,1 1 iiiii iIII I llII II I

0.0 III II

:--20 -i0 0 10 20SReconstr. Angle

- ': lllInrm 39. Angular wmitii4 nwmur==ft for 0 . -= 0 and 0 - 9. E -= 15.9.

-- 1 0

A progression of plots shown in figure 3-10 presents quite clearly the increasing efficiency

A of the side lobes as the index of modulation increases. The exposure energies vary from 3.3 to

- 223.4 mJ/cm, while the index of modulation varies from .02 to greater than .06. While the

efficiency of the center lobe increases and decreases as expected, though to a lesser degree than

Kogelnik's theory predicts, the half-power bandwidth remains the same. The calculated value is

6.1 degrees and the measured value is approximately 8 degrees.

.34.

-p." %

Eta1.0 l

to. 0

-' 1/I

0 05 15 25 35 45

Reconstr. Angle

g., m 3m0. Anguar mitvity mn turmes for . = -0 16. E 0 iS.8.a . o o

- The wavelength sensitivity was measured for a hologram with incident angles of

. - 0 - 16. The diffraction efficiency was peaked at 21.2 degrees for the green 514.5 nma o

light and then was measured for that same angle with wavelengths of 442.0, 488.0 and 632.8

nim. The result is shown in figure 3-11. The half-power bandwidth is measured to be

approximately 180 nm; the calculated value is 142 nm. The experiment itself was not very exact

and Kogelnik's theory is also approximate, so the correlation is acceptable.

.33-* .... , ..

Eta

i.-

S0.0 111111 lili,l1111111111l11 111111IIIIIII1 I

440.0 490.0 540.0 590.0 640.0

Wavelength (nm)

Rpgm 3-U. WavW=X&t =Mitvity mmimmmt-q vsX

3.4.3 ShrinkageJ

At different stages in processing, the thickness of DMP-128 changes. During activation the

emulsion absorbs water and increases in thickness. As the exposure is made with the emulsion

in this state, the thickness T at this point is the thickness for hologram formation. The

measured thickness after processing is seven microns. Not being able to measure the thickness

during exposure, it must be calculated from the theory in Chapter 2. Solving Eqs. 2.48a & b

.36-

for an angle of 9 degrees, the shrinkage factor s is seen to be .82. This translates to a

shrinkage of about 18%. As a rough confirmation of this shrinkage factor, reflection holograms

recorded in the red "play back" in the green-blue region. In reflection holograms the fringe

planes are parallel to the substrate, so the period changes directly with the thickness. A

spectrophotometer measurement of the absorption by an in-line reflection hologram constructed

with the 632.8 m line of a He-Ne laser showed a peak absorption around 480 nm, so a rough

estimate of the shrinkage factor is s = 480/632.8 = .76. Since the object signal was not a plane

wave in this case, this result must be regarded as a rough estimate only.

3.4.4 Resolution

The resolution requirements for phase transmission holograms constructed with a wavelength

of 632.8 nm range from 0 cycles/mm (for an inter-beam angle of zero degrees) to 3160

cycles/mm (for an inter-beam angle of 180 degrees). The range of resolutions used in this study

extended only from 410.4 to 1335.6 cycles/mm. These spatial frequencies were well within the

resolution capabilities of DMP-128.

3.4.5 Handling and processing

DMP-128 is an extremely easy film to use. The film can be stored for up to a year at a

relative humidity less than about 35%. Some of the film used in this experiment was 6 months

old at the time of exposure; a maximum diffraction efficiency of 90% was achieved with one of

these plates. With the exception of silver halide, most other films have a shelf life of days or

hours, not months, once they are formulated or coated on a substrate. After flooding with light,

DMP-128 can be developed and fixed with one chemical bath and then dried. Some films, one

of which is the Dupont photopolymer, can develop themselves with no processing and thus

produce near real-time holograms, but they require fixing in order to prevent the hologram from

degrading in a matter of hours or days. DMP-128 must be fixed and developed chemically, but

the whole process requires only five to six minutes and the holograms show little sign of

.37-

• '- " . " "'' """- "" - ,' -' 'W .' " " "- " " . .. . . .. ' " , ,- , ", * ,1 Z

degrading, even under conditions of high humidity. Another advantage of DMP-128 is the

-option of using safelights during all stages of exposure and processing. In the case of red-

.' Z-, sensitized film, the laboratory may be illuminated with blue safe-lights even after the emulsion is

activated.

The activation of the film in a controlled humidity chamber must be determined

experimentally, but once the optimal activation time has been found the incubation period need

only be held constant; the film can be very activated in an easily reproducible manner. In order

to prevent the loss or additional absorption of water after activation, the laboratory must be

maintained at a relative humidity near 51%. The shrinkage discussed above is a disadvantage,

but with additional processing baths, this can be at least partially corrected. DMP-128 has been

observed to crack along the fringe planes when overexposed or subjected to repeated drying.

This is a result of stressing the material too much and can generally be avoided.

.13

V..

.36

Chapter 4. CONCLUSIONS

In this thesis a new holographic recording system was tested. Polaroid's DMP-128 film is a

photopolymer medium which produces phase holograms. The phase change is caused by the

polymerization of monomers by photo-initiation. A hologram with a diffraction efficiency of

90% was produced. An index of modulation in excess of .06 was achieved for high exposure

energy without harming the integrity of the emulsion. Regions of linearity for V plotted

against visibility and exposure were shown. The mechanisms responsible for diffraction by the

photopolymer were investigated; both surface relief and volume phase modulation are observed

to be present. Wavelength and angular sensitivity were measured and found to agree closely

with Kogelnik's coupled wave theory. Resolution and the extreme ease of handling and

processing of DMP-128 werealso discussed.

4.1 Sugesadons for Further Research

All of the holograms fabricated in the process of this research were formed with X. = 632.8

nm. The emulsion, however, is sensitive over a broader range of wavelengths than this. Others

have obtained an estimate for the spectral sensitivity of DMP-128 [12], but a rigorous experiment

has yet to be conducted to verify this. To accomplish this, holograms should be constructed at a

given intensity for a range of wavelengths and then be measured for diffraction efficiency.

Additional investigation could be directed toward a similar characterization of the blue- and

green-sensitized formulations of DMP-128. The more complicated problem of reflection

holography can also be explored much like transmission has been in this work.

The major thrust of any additional work should be centered around the processing of the

film. Variables such as effects of flooding time and delay time before flooding need to be

measured to check for diffusion of the monomer. The intensity and duration of the flood also

merits investigation. The chemical processing could be tested. Variations in the chemical

-39-

* .W, V ~ %

components should be tried and their effects noted. Closely linked with this would be an

-, investigation into methods to swell the emulsion back to its thickness during exposure.

40,

----

References

[11 Smith, H. M., Principles of Holography, 2nd ed., John Wiley & Sons, New York, 1975.

[21 Smith, H. M., ed., Holographic Recording Materials, Springer-Verlag, Berlin, 1977.

[3] Collier, Robert J., et al., Optical Holography, Academic Press, Inc., Orlando, 1971.

(4] Kogelnik, H., "Coupled Wave Theory for Thick Hologram Gratings", Bell System

Technical Journal, 48:9, Nov. 1969, pp. 2909-2947.

[5] Guenther. B. D., to be published.

[61 Rick Feinberg, "An Interview with Richard T. Ingwal: Photopolymers for Holography."

Optical Engineering Reports, No. 31, July 1986, pp. 1, 4.

(7] R.T. Ingwall, A. Stuck, W.T. Vetterling, "Diffraction Properties of Holograms Recorded

in DMP-128", Polaroid technical report no. 615-05.

[8] Curran, R. K. and Shankoff, T. A., "The Mechanism of Hologram Formation in

Dichromated Gelatin", Applied Optics 9, No. 7, July 1970, pp. 1651-7.

[91 Ingwall, R. T. and Fielding, H. L., "Hologram Recording with a New Polaroid

Photopolymer Recording System", SPIE Vol. 523 Applications of Holography (1985), pp.

306-12.

[101 Vilkomerson, D. H. R. and D. Bostwick, D., "Some Effects of Emulsion Shrinkage on a

Hologram's Image Space", Applied Optics 6, No. 7, July 1967, pp. 1270-1.

-41.

.. p* , ~ . pr

[111 Lin, L. H., "Method of Characterizing Hologram-Recording Materials", Journal of the

-Optical Society of America, Vol. 61, No. 2, February 1971, pp. 203-8.

.

[121 Stone, Thomas, personal communication.

[13] Norton, M. C., "Holographic Applications of Polaroid DMP-128", no published date.

- 42-

-42-

Iv~n"ba

pI

V III UIL